Constraining Planet Structure and Composition from Stellar Chemistry: Trends in Different Stellar Populations N

Astronomy & Astrophysics manuscript no. santos˙31359 c ESO 2017 November 3, 2017

Constraining planet structure and composition from stellar chemistry: trends in different stellar populations N. C. Santos1,2, V. Adibekyan1, C. Dorn3, C. Mordasini4, L. Noack5,6, S. C. C. Barros1, E. Delgado-Mena1, O. Demangeon1, J. Faria1,2, G. Israelian7,8, and S. G. Sousa1

1 Instituto de Astrof´ısica e Cienciasˆ do Espac¸o, Universidade do Porto, CAUP, Rua das Estrelas, 4150-762 Porto, Portugal 2 Departamento de F´ısica e Astronomia, Faculdade de Ciencias,ˆ Universidade do Porto, Rua do Campo Alegre, 4169-007 Porto, Portugal 3 University of Zurich, Institut of computational sciences, Winterthurerstrasse 190, CH -8057 Zurich¨ 4 Physikalisches Institut, University of Bern, Gesellschaftsstrasse 6, CH-3012 Bern, Switzerland 5 Department of Reference Systems and Geodynamics, Royal Observatory of Belgium (ROB), Avenue Circulaire 3,1180 Brussels, Belgium 6 Institute of Geological Sciences, Freie Universitat¨ Berlin, Malteserstr. 74-100, 12249 Berlin, Germany 7 Instituto de Astrof´ısica de Canarias, C/V´ıa Lactea´ s/n, 38205 La Laguna, Tenerife, Spain 8 Universidad de La Laguna, Dept. Astrof´ısica, E-38206 La Laguna, Tenerife, Spain Received date / Accepted date

Abstract

Context. The chemical composition of stars that have orbiting planets provides important clues about the frequency, architecture, and composition of exoplanet systems. Aims. We explore the possibility that stars from different galactic populations that have different intrinsic abundance ratios may produce planets with a different overall composition. Methods. We compiled abundances for Fe, O, C, Mg, and Si in a large sample of solar neighbourhood stars that belong to different galactic populations. We then used a simple stoichiometric model to predict the expected iron-to-silicate mass fraction and water mass fraction of the planet building blocks, as well as the summed mass percentage of all heavy elements in the disc. Results. Assuming that overall the chemical composition of the planet building blocks will be reflected in the composition of the formed planets, we show that according to our model, discs around stars from different galactic populations, as well as around stars from different regions in the Galaxy, are expected to form rocky planets with significantly different iron-to-silicate mass fractions. The available water mass fraction also changes significantly from one galactic population to another. Conclusions. The results may be used to set constraints for models of planet formation and chemical composition. Furthermore, the results may have impact on our understanding of the frequency of planets in the Galaxy, as well as on the existence of conditions for habitability. Key words. (Stars:) Planetary systems, Planets and satellites: composition, Techniques: spectroscopy, Stars: abundances

————————————————- up to ∼+0.5 dex. Thick-disc stars typically have lower metallicities than their thin-disc counterparts. More specifically, they present higher values of α-element1 abundances (for a recent pa- 1. Introduction per, see Adibekyan et al. 2013a). Finally, halo stars are usually objects of lower metallicity, which also often present α element The study of stars hosting planets is providing a huge amount enhancement. They are commonly identified using dynamical of information about the processes of planetary formation and approaches (Bensby et al. 2003a). The kinematical and chem- evolution (see e.g. Mayor et al. 2014). The dependence on the ical properties (in particular the abundance ratios) of these three frequency of planets with the stellar metallicity and mass (e.g. populations reflect their origin, age, and the galactic formation Santos et al. 2004; Fischer & Valenti 2005; Johnson et al. 2007; process (e.g. Haywood et al. 2013a); see Appendix A for more arXiv:1711.00777v1 [astro-ph.EP] 2 Nov 2017 Sousa et al. 2011b; Buchhave et al. 2012), for example, has details. been suggested as strong evidence in favor of the hypothesis of the core-accretion model as the dominant giant planet formation Recent studies suggest that the abundances of specific chem- process (e.g. Mordasini et al. 2012a). The architecture of plane- ical species in the stellar photosphere may give clues about the tary systems and its dependence on the metal content of the stars internal structure and composition of the planets. This is true further provides indications about the processes involved in the both for giant planets (Guillot et al. 2006; Fortney et al. 2007) planet migration (e.g. Dawson & Murray-Clay 2013; Adibekyan and for their rocky counterparts (e.g. Bond et al. 2010; Delgado et al. 2013b; Beauge´ & Nesvorny´ 2013). Mena et al. 2010; Dorn et al. 2015; Thiabaud et al. 2015; Santos The stars we observe in the solar neighbourhood can be di- et al. 2015; Dorn et al. 2017). Stars from different galactic pop- vided into three galactic populations: the thin-disc, the thick- disc, and the halo population. Most stars are members of the 1 Elements for which the most abundant isotopes are integer multi- younger thin-disc component, ranging in [Fe/H] from ∼−0.8 ples of 4, the mass of a helium nucleus (α particle)

1 N. C. Santos et al.: Constraining planet structure and composition from stellar chemistry: trends in different stellar populations ulations may thus present different planet frequencies, and the [Fe/H]¡−0.2 dex) and its α-rich metal-rich counterpart (20 stars planets orbiting them may present different composition trends with [Fe/H]≥ −0.2 dex), hereafter called hαmr. Finally, 3 stars (e.g. Haywood 2008; Adibekyan et al. 2012a; Frank et al. 2014; in our sample were identified as belonging to the galactic halo Adibekyan et al. 2015, 2016a). following the kinematic criteria of Bensby et al. (2003a). They In this context, the present paper investigates whether stars were treated separately since halo stars in the solar neighbour- that come from different galactic populations and have differ- hood are also known to be mainly rich in α elements (but see ent chemical composition are expected to form planet building Nissen & Schuster 2010). blocks (or planets) with different compositions. In Sect. 2 we present the data selected for this study, including detailed chemical abundances for several elements. In Sect. 3 we then describe 3. Model our model, applying it to the stars in different galactic populations in Sect. 4. Finally, in Sect. 5 we discuss our results in face The model we used here is the same as was used in Santos of the expected planet populations in the galaxy, including the et al. (2015). In brief, it makes use of the abundances of the prospects for life-bearing worlds. rock-forming elements Fe, Si, Mg, C, and O, together with H and He, and assumes that these are the most relevant to control the species expected from equilibrium condensation models (Lodders 2003; Seager et al. 2007), such as H2, He, H2O, CH4, 2. Data 3 Fe, MgSiO3, Mg2SiO4, and SiO2 . In other words, in our model To explore the effect of different initial stellar abundances on we only include the mineral phases of the main rock-forming el- the planet composition, we need to define a sample of stars for ements that dominate the crust, the upper and lower mantle, and which precise abundances have been determined. As we show the core of an Earth-like planet interior (see e.g. McDounough below, our model needs abundance values for Fe, Si, Mg, C, and & Sun 1995; Sotin et al. 2007). A simplified model for the ex- O as input. To build this sample, we started from the work of pected mass fractions of different compounds using these species Adibekyan et al. (2012b). This study, based on spectra with high is thus a reasonable approach. In this case, the molecular abun- signal-to-noise (S/N) ratios and high resolution obtained with dances and therefore the mass fraction can be found from the the HARPS spectrograph, provides abundances of Fe, Si, and atomic abundances with simple stoichiometry, as discussed in Mg for 1111 stars in a volume-limited sample. Oxygen abun- Santos et al. (2015); see also Bond et al. (2010); Thiabaud et al. dances were then added from the study of Bertran de Lis et al. (2015); Unterborn & Panero (2016). (2015). The values derived using the 6158 Å oxygen line were We note that no star in our sample has values of Mg/Si¿2, in preferred, as these have been shown by the authors to be more which case, Si would be incorporated in olivine and the remain- precise. Finally, for C we used the carbon values recently de- ing Mg would enter in other minerals, mostly oxides. Our simple rived by Suarez-Andr´ es´ et al. (2017). All these abundances were model does not take these cases into consideration. Moreover, derived based on same set of uniform stellar atmospheric param- ten stars were found to have C/O ratios above 0.8: above this eters (namely Te f f and log g, from Sousa et al. 2008, 2011b,a). value, the mineralogy is expected to be significantly different All abundances listed in these papers (as well as the stel- (Bond et al. 2010), with carbides forming instead of the sili- lar parameter analysis) were computed relative to the Sun. cates; planet building blocks would then be strongly enriched They were transformed into absolute abundances assuming the in carbon. Since only one star was found with C/O above 1 solar composition as given in Asplund et al. (2009) for Fe (C/O=1.14), and given the typical (high) errors in the derivation (log =7.50), Mg (log =7.60), and Si (log =7.51), and as given of abundances for these species (see Bertran de Lis et al. 2015; by Bertran de Lis et al. (2015) and Suarez-Andr´ es´ et al. (2017) Suarez-Andr´ es´ et al. 2017), we decided to keep these stars in for O (log =8.71) and C (log =8.50).2 For helium, the adopted the sample. In any case, observations suggest that only a small value was taken from Lodders (2003, log =10.93). fraction of the stars in the solar neighbourhood have C/O¿0.8 In total, we have 535 stars for which precise values of abun- (Fortney 2012; Brewer & Fischer 2016). dances for Fe, Si, Mg, C, and O have been obtained. These stars The simple relations presented in Santos et al. (2015) (see represent the solar neighbourhood sample well. In order to avoid also Appendix B) allow us to compute the expected mass frac- 4 strong systematic effects or errors in the abundances caused by tions, in particular, the iron-to-silicate mass fraction ( firon) , uncertainties in the line-lists and model atmospheres as we move the water mass fraction (w f ), and the summed mass percent away from the solar values (see e.g. Adibekyan et al. 2012b; of all heavy elements (Z) expected for the planetary building Bertran de Lis et al. 2015), we decided to further cut our sample blocks/grains: to include only stars with a temperature of ±300 K around solar firon = mFe/(mFe + mMgSiO3 + mMg2SiO4 + mSiO2) (1) (we assume Te f f ( )=5777 K). This left us with 371 stars. To classify the stars into different galactic populations, we w f = mH2O/(mH2O + mFe + mMgSiO3 + mMg2SiO4 + mSiO2) (2) used the chemical boundary discussed in Adibekyan et al. Z = (mCH4 + mH2O + mFe + mMgS iO3+ (2012b). According to this, 303 of the 371 stars belong to the thin , (3) mMg2S iO4 + mS iO2)/Mtot disc, while 68 have enhanced α-element abundances. This latter pattern is typical of thick-disc stars of our Galaxy. However, for where mX = Nx ∗µX, Mtot = NH ∗µH + NHe ∗µHe + NC ∗µC + NO ∗ α-rich metal-rich stars ([Fe/H]¿−0.2 dex), there is no consensus µO + NMg ∗ µMg + NS i ∗ µS i + NFe ∗ µFe, and NX represents the about which galactic population they belong to (Adibekyan et al. number of atoms of each species X, and µX their mean molecular 2011a; Bensby et al. 2014). We therefore divided the 68 stars weights. All NX values are computed relative to hydrogen. into two different groups: the thick-disc population (48 stars with These variables are expected to have an important influence on the planet structure and radius (Dorn et al. 2017). They are 2 The value [X/H], where X is a specific element, is defined as [X/H] N N = log X - log ( X ) , where N is the number of atoms. The values of 3 NH NH There are more silicate forms, but these are the most relevant. log are defined as log =log NX + 12. 4 Not taking into account the iron silicates. NH

2 N. C. Santos et al.: Constraining planet structure and composition from stellar chemistry: trends in diﬀerent stellar populations

Table 1. Average values and standard deviations for firon and the and water mass fraction. Average values of firon over the differ- water mass fraction in the different galactic populations. ent populations vary between 22.5 and 23.1 for the metal-poor thick-disc and halo stars, respectively, and rise up to 32.5 for the Population Average Std. metal-rich thin-disc population. Water mass fractions also vary firon from average values of ∼58% for the thin-disc metal-rich stars Thin Disc 31.974 1.750 to 76% and 83% for the metal-poor thick-disc and halo. Thin Disc ([Fe/H]¡−0.2) 29.430 1.550 Several conclusions can be drawn from comparing different Thin Disc ([Fe/H]≥ −0.2) 32.514 1.240 groups of thin-disc stars. First, and as expected, the value of firon Thick Disc ([Fe/H]¡−0.2) 22.464 1.742 and w f for stars of the metal-rich thin-disc population (where the hαmr 28.727 1.338 Sun is included) suggest that these should be able to host planets Halo† 23.110 2.884 similar in composition to the solar system planets. Metal-poor w f thin-disc stars, on the other hand, are expected to have lower Thin Disc 59.713 7.106 iron and higher water mass fractions than the fractions expected Thin Disc ([Fe/H]¡−0.2) 68.014 7.116 Thin Disc ([Fe/H]≥ −0.2) 57.953 5.724 for the Sun. The relatively small increase in the water fraction is Thick Disc ([Fe/H]¡−0.2) 76.172 5.448 related to the relatively higher [O/Fe] ratios observed in metal- hαmr 62.591 7.194 poor thin-disc stars (Bertran de Lis et al. 2015) when compared Halo† 83.990 4.115 to their metal-rich counterparts. The lower firon reflects the de- Z crease in metallicity and increase in the α-element abundances. Thin Disc 1.508 0.597 According to our results, the metal-poor thick-disc popula- Thin Disc ([Fe/H]¡−0.2) 0.818 0.181 tion is expected to produce planets with much lower iron mass Thin Disc ([Fe/H]≥ −0.2) 1.655 0.550 fractions (that may be translated into smaller cores). The water Thick Disc ([Fe/H]¡−0.2) 0.870 0.233 mass fraction in these stars, however, is higher than the frac- hαmr 1.773 0.444 tion found in thin-disc objects. This is again expected as these Halo† 0.808 0.082 stars present on average higher oxygen abundances than thin- † We only have three halo stars, which limits the conclusions for this disc stars of the same [Fe/H]. Interestingly, our results also sug- specific galactic population. gest that hαmr stars might produce planets with values of firon and w f intermediate between the thin-disc and the metal-poor thick-disc stars. This reflects their high α-element abundances (O, C, Si, and Mg) when compared to thin-disc stars of the same also expected to provide relevant information about some pa- metallicity, which leads to a relative increase in water mass frac- rameters relevant for the planet formation process, such as the tion but a decrease of f . mass fraction of all heavy elements and the ice mass fraction in iron solid planets, or giant planet cores that form beyond the water We only have three halo stars in our sample, which limits ice-line. our conclusions regarding this population. However, and as ex- We should note that in the calculations above we assume that pected, our model indicates that they might produce planets with the composition of H, C, N, O, Mg, Si, and Fe dominates the a low iron mass fraction while being water rich. To our knowl- composition of the solid material. This is likely a good approxi- edge, there is no planet detected so far that orbits a halo star. mation, as in the Sun these elements represent the main contrib- Finally, the average values of Z for the different populations utors to the overall composition (see abundances in e.g. Asplund range from ∼0.8% to ∼1.7% (a factor of ∼2), with the individ- et al. 2009). ual values ranging from ∼0.5% up to ∼3%. As expected, metal- The model predicts that planet building blocks for solar sys- poor thin-disc and halo stars have the lowest average values of Z, while the remaining populations have higher values, even if tem have firon = 33%, w f = 60%, and Z = 1.26%. The value of f is compatible to the value observed in the terrestrial planets a large spread is observed in each population. Z is expected to iron be related to the planet formation efficiency. Increasing Z may (see the discussion below), while w f and Z are similar to the values derived in Lodders (2003, 67.11% and 1.31%, respectively). increase the probability of forming terrestrial-like planets or the In Appendix C we present some simple relations to compute icy/rocky cores of giant planets. This fact is behind the usual in- the values of f and Z based on the stellar abundances. terpretation for the clear metallicity-giant planet correlation that iron is observed (e.g. Santos et al. 2004; Fischer & Valenti 2005). Interestingly, even if such a clear correlation has not been found 4. Results for stars hosting the lower mass planets (e.g. Sousa et al. 2011b; Buchhave et al. 2012), hints exists that the overall metallicity In Fig. 1 we present the distributions of iron and water mass still plays a role in this planet mass regime (e.g. Adibekyan et al. fractions (top and middle panels) for the stars in our sample, 2012a; Wang & Fischer 2015; Zhu et al. 2016). as derived with the model described above. The bottom panels present the values of Z. The left panels present the comparison of the four galactic populations mentioned above, and the right 5. Discussion: planet composition, frequency, and panels present the comparison between thin-disc stars of differ- habitability ent metallicity. This separation is motivated by the fact that low- metallicity thin-disc stars present an increasing α-element en- The results presented above suggest that solar neighbourhood hancement as [Fe/H] decreases (e.g. Adibekyan et al. 2012a). In stars from different galactic populations whose abundance ra- Table 1 we present the average and standard deviation values for tios are different may be able to produce planets, or at least the different populations. the planet building blocks, that have different intrinsic compo- The results presented in Fig. 1 and in the table show that sitions. Thick-disc stars in our Galaxy, for example, are known (on average) we can expect planet building blocks in different to be older than their thin-disc counterparts (e.g. Haywood et al. galactic populations to have significantly different values of iron 2013a). Stars in different galactic regions (inner vs. outer disk

3 N. C. Santos et al.: Constraining planet structure and composition from stellar chemistry: trends in diﬀerent stellar populations

Figure 1. firon (upper panels), w f (middle panels), and Z (lower panels) mass fractions distributions for the different populations in the Galaxy. and stars with different heights above the galactic plane) also or future) or in different galactic regions may have a signifi- present different abundance ratios (e.g. Hayden et al. 2015; cantly different composition trend. The planet formation effi- Haywood et al. 2016). As has been discussed in some recent ciency around different populations of stars may also be different works (e.g. Frank et al. 2014; Adibekyan et al. 2016a,b), this (Adibekyan et al. 2012a). may imply that planets formed in different galactic ages (past

4 N. C. Santos et al.: Constraining planet structure and composition from stellar chemistry: trends in diﬀerent stellar populations

Understanding whether the initial conditions for planet for- or internal structure of a final differentiated planet (or chemical mation depend on the galactic population can also constrain the distribution within the planet). The composition of a planet of modelling of planet formation and planet structure. For instance, course depends on the region of the proto-planetary disc where the overall amount of solid material (Z) and the expected com- it formed as well as on its migration path (e.g. Mordasini et al. position of the building blocks ( firon and w f ) can be used as a 2012b; Carter-Bond et al. 2012). Physical processes, includ- prior to understand the frequency and populations of planets ex- ing evaporation and collisional stripping, may also be able to isting in the solar neighbourhood from planet population synthe- change the overall composition of a planet (including its core- sis models (e.g. Mordasini et al. 2012b). Furthermore, priors on to-mantle fraction), as likely happened to Mercury (Benz et al. the planet composition can be set when modelling a planet based 1988; Marcus et al. 2010a). Moreover, the compositional evo- on its mass-radius relation (e.g. Dorn et al. 2017), as long as the lution of a planet depends on the accretion and differentiation abundances for some elements are known in the host star, or if history for which the understanding of the compositional model the stellar population is deduced from kinematic studies (e.g. and the cooling history of the primitive body are key (Rubie et al. with GAIA), for example. 2015; Fischer et al. 2017). We note that our basic assumption is that the chemical com- Regarding the water content, and given the spread in wa- position of the (rocky) planets is intimately related to the chem- ter fractions in our solar system’s terrestrial planets, we should ical composition of the star. This is likely a good approximation also add that the origin of the water in our own planet Earth is from a statistical approach, as in the solar system the relative still strongly debated, and several external processes (e.g. comet amount of refractory elements is correlated between meteorites, infall or strong stellar activity) that occurred during and after the solar photosphere, and the terrestrial planets Earth, Venus, planet formation may likely significantly change the amount of and Mars (e.g. Morgan & Anders 1980; Lodders 2003; Drake & water on the surface of a planet (Marcus et al. 2010b; Luger et al. Righter 2002; Lodders & Fegley 1998; Khan & Connolly 2008; 2015). The values of w f derived are therefore expected to be in- Sanloup et al. 1999). This is also found from models (see e.g. dicative of the amount of water available in the proto-planetary Thiabaud et al. 2015), even if exceptions may exist (Dorn et al. disc; although this probably correlates with the final water con- 2017). Finally, observations of rocky exoplanets also seem to tent of the planets, strong scatter is expected. Water accumu- suggest that they tend to follow the Earth composition line (e.g. lates in the outer part of the disc during the later condensation Motalebi et al. 2015), in agreement with the assumptions taken of volatile atoms compared to heavier elements such as silicates here (see also Santos et al. 2015). In this context, it would now be and iron, which make up the main building blocks of the inner interesting to understand, for instance, if the mentioned result is part of the proto-planetary disc. Even though the outer planets compatible with the radius of planets orbiting metal-poor thick- Jupiter, Saturn, Uranus, and Neptune contain mostly hydrogen, disc stars (e.g. EPIC 210894022b/K2-111b – Fridlund et al. helium, and methane above their rocky core, the compositions 2017). Exceptions to this trend may also have been found. These of several of their moons are dominated by water and ice. The can be the cases of LHS 1140 b (Dittmann et al. 2017), for which amount of available water can also be related to the planet (or the best-fit model implies a higher core mass fraction (even if core) formation efficiency beyond the ice line, as it will control compatible with Earth-like fractions within the errors), or the the amount of condensates in this region. recently discovered very short period K2-106 b (Guenther et al. Overall, our results suggest that stars in different galactic 2017). On the positive side, recent results suggest that the star populations may produce planets with different core mass frac- TRAPPIST-1 may be a thick-disc object (Burgasser & Mamajek tions and water contents. It is thus interesting to discuss the im- 2017). Curiously, the planets discovered in this system that have plications of this result for astrobiology. It has been suggested a good mass estimate have been proposed to have a low den- that large core mass fractions may inhibit plate tectonics (Noack sity (favouring a volatile-rich composition – Gillon et al. 2017), et al. 2014). Plate tectonics is believed to be important for the a result compatible with our model. It would be very inter- evolution of complex life since it helps to maintain the mag- esting to investigate the detailed abundances of these specific netic field, replenishes the surface with nutrient-rich soil, and stars in face of the results obtained above. New planet detec- stabilizes the long-term global carbon cycle. Furthermore, in the tions around bright nearby stars, expected with missions such as absence of plate tectonics, large cores can suppress outgassing TESS, CHEOPS, and PLATO, will certainly allow us to address of greenhouse gases on stagnant-lid planets (Noack et al. 2017). this field. Finally, water has also been discussed to be a key ingredient for We also assume here that no internal or external physical pro- promoting plate tectonics (Korenaga 2010) and plays a crucial cess are able to significantly alter the initial stellar composition. role for the surface habitability of rocky planets as well as for Planet engulfment processes have been suggested to be responsi- their interior evolution. Water in the mantle significantly reduces ble for specific stellar abundance patterns (Israelian et al. 2001), both silicate melting temperatures and mantle viscosity, and also even if such events may be rare. Furthermore, the magnitude of influences the chemistry in the mantle. Different planet compo- this effect on the stellar abundances of G-type stars (with deep sitions may in this context alter the width of the habitable zones, convective envelopes) is expected to be small when compared since plate tectonics is related to the capacity to degass CO2. with the typical uncertainties in the abundances (e.g. Santos et al. This may have implications for the definition of the so-called 2003). Other less well understood effects, such as element dif- Galactic habitable zone (e.g. Lineweaver et al. 2004; Prantzos fusion, could also affect specific stellar abundances (e.g. One-¨ 2008; Carigi et al. 2013; Gonzalez 2014; Spitoni et al. 2017). hag et al. 2014), but the magnitude of this effect is in any case Since the quantity of available water in a planet may be related to expected to be small for solar-type stars (Onehag¨ et al. 2014; the relative water content existing in the planet building blocks, Gonzalez 2014). These effects need to be kept in mind, however, the values derived in this paper may also give us some indica- even if they may only be able to introduce minor changes to the tions about the prevalence of water worlds (Leger´ et al. 2004; original chemical abundances. Simpson 2017). We also stress that the results discussed here can be used Acknowledgements. This work was supported by Fundaçao˜ para a Cienciaˆ to estimate the composition of the planet building blocks, but e a Tecnologia (FCT, Portugal) through the research grant through national they might not be directly applicable to the final composition funds and by FEDER through COMPETE2020 by grants UID/FIS/04434/2013

5 N. C. Santos et al.: Constraining planet structure and composition from stellar chemistry: trends in diﬀerent stellar populations

& POCI-01-0145-FEDER-007672, PTDC/FIS-AST/1526/2014 & POCI-01- Haywood, M., Di Matteo, P., Lehnert, M. D., Katz, D., & Gomez,´ A. 2013b, 0145-FEDER-016886 and PTDC/FIS-AST/7073/2014 & POCI-01-0145- A&A, 560, A109 FEDER-016880. P.F., S.B., N.C.S. e S.G.S. acknowledge support from FCT Haywood, M., Lehnert, M. D., Di Matteo, P., et al. 2016, A&A, 589, A66 through Investigador FCT contracts nr. IF/01037/2013CP1191/CT0001, Israelian, G., Santos, N. C., Mayor, M., & Rebolo, R. 2001, Nature, 411, 163 IF/01312/2014/CP1215/CT0004, IF/00169/2012/CP0150/CT0002, and Ivezic,´ Z.,ˇ Beers, T. C., & Juric,´ M. 2012, ARA&A, 50, 251 IF/00028/2014/CP1215/CT0002. V.A. and E.D.M. acknowledge support from Johnson, J. A., Butler, R. P., Marcy, G. W., et al. 2007, ApJ, 670, 833 FCT through Investigador FCT contracts nr. IF/00650/2015/CP1273/CT0001, Juric,´ M., Ivezic,´ Z.,ˇ Brooks, A., et al. 2008, ApJ, 673, 864 IF/00849/2015/CP1273/CT0003 and by the fellowship SFRH/BPD/70574/2010, Khan, A. & Connolly, J. A. D. 2008, Journal of Geophysical Research: Planets, SFRH/BPD/76606/2011 funded by FCT and POPH/FSE (EC). PF further 113, n/a, e07003 acknowledges support from Fundaçao˜ para a Cienciaˆ e a Tecnologia (FCT) in Kordopatis, G., Wyse, R. F. G., Gilmore, G., et al. 2015, A&A, 582, A122 the form of an exploratory project of reference IF/01037/2013CP1191/CT0001. Korenaga, J. 2010, ApJ, 725, L43 L.N. has been funded by the Interuniversity Attraction Poles Programme Leger,´ A., Selsis, F., Sotin, C., et al. 2004, Icarus, 169, 499 initiated by the Belgian Science Policy Office through the Planet Topers Lineweaver, C. H., Fenner, Y., & Gibson, B. K. 2004, Science, 303, 59 alliance and by the Deutsche Forschungsgemeinschaft (SFB-TRR 170). C.M. Lodders, K. 2003, ApJ, 591, 1220 acknowledges the support from the Swiss National Science Foundation under Lodders, K. & Fegley, B. 1998, The planetary scientist’s companion / Katharina grant BSSGI0 155816 “PlanetsInTime”. 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6 N. C. Santos et al.: Constraining planet structure and composition from stellar chemistry: trends in different stellar populations scale-height and short scale-length5 (e.g. Bovy et al. 2012). Most This equation can be used to predict the iron mass contents stars in the solar neighbourhood6 are members of the younger for the planetary building blocks when the values of [Si/Fe] are thin-disc component, and they range in [Fe/H] from ∼-0.8 up known. to ∼+0.5 dex (Kordopatis et al. 2015; Adibekyan et al. 2013a). Similarly, in Fig. C.1 (middle panel), we plot the relation be- Thick-disc and halo stars typically have lower metallicities than tween the values of Z and an index defined as their thin-disc counterparts. (Mg) (S i) (Fe) There is no obvious predetermined way to distinguish be- Index1 = log 10 + 10 + 10 . (C.2) tween different stellar populations in the solar neighbourhood. However, since chemistry is a relatively more stable property of Here (X) denotes the abundance of a given element. The choice of Mg, Si, and Fe to build this index comes from the fact a star than its spatial positions and kinematics, it is becoming that these are the easiest to measure in a solar-type star of the increasingly clear that a dissection of the Galactic discs based elements we studied here. only on stellar abundances is superior to kinematic separation (see Navarro et al. 2011; Adibekyan et al. 2011b). Stellar ages Z = 1.596 Index3 − 34.971 Index2 can also be effectively used to separate the thin- and thick-disc 1 1. (C.3) stars (e.g. Haywood et al. 2013b), although they are very diffi- +255.799 Index1 − 623.802 cult to obtain in high precision. Halo stars are commonly identi- This relation can be used to estimate the value of Z in any fied using dynamical approaches (e.g. Bensby et al. 2003b) since solar neighbourhood star when the abundances of these three el- these stars share similar chemical properties with their thick-disc ements are known. counterparts. The kinematical and chemical properties (in partic- Finally, when the abundances for C and O are also available, ular the abundance ratios) of these three populations reflect their we can define the index above as origin, age, and the galactic formation process (e.g. Ivezic´ et al. 2012). (Mg) (S i) (Fe) (C) (O) We refer to Fig. 1 of Buser (2000) for a good scheme of the Index2 = log 10 + 10 + 10 + 10 + 10 . different Galactic populations. (C.4) In this case, a cubic fit to the data (see Fig. C.1, lower panel) Appendix B: Our model equations provides a much tighter relation: Our model is based on the following stoichiometric relations. Z = 2.280 Index3 − 57.831 Index2 2 2. (C.5) When NMg >NS i (see e.g. Bond et al. 2010; Thiabaud et al. 2015; +490.140 Index2 − 1387.773 Unterborn & Panero 2016),

NO = NH2O + 3NMgSiO3 + 4NMg2SiO4 (B.1)

NMg = NMgSiO3 + 2NMg2SiO4 (B.2)

NSi = NMgSiO3 + NMg2SiO4 (B.3)

NC = NCH4 , (B.4) otherwise, when NMg ≤NS i,

NO = NH2O + 3NMgSiO3 + 2NSiO2 (B.5)

NMg = NMgSiO3 (B.6)

NSi = NMgSiO3 + NSiO2 (B.7)

NC = NCH4 . (B.8) Inverting these equations and adding the observed stellar abundances allows us to derive the ratios analysed in this work.

Appendix C: Predicting the iron mass fraction

In Fig. C.1 (upper panel) we present the derived firon for all the stars in our sample as a function of [Si/Fe]. We divided the stars into different populations, following the definition discussed in Sect. 2. The plot illustrates the dependence of our model on the different chemical abundances. In particular, it shows that firon is strongly dependent on the [Si/Fe] ratio7. A cubic fit to the data provides the relation f = 253.522 [S i/Fe]3 − 61.149 [S i/Fe]2 . (C.1) −53.342 [S i/Fe] + 33.240

5 We note, however, that previous studies have obtained longer scale- lengths for the stellar density proﬁle of the thick disc (e.g. Juric´ et al. 2008). 6 This value is around ∼50% if we consider the whole Galaxy (e.g. Snaith et al. 2015). 7 The same correlation is also obtained using the [Mg/Fe] ratio, as these two are tightly related. However, since there are more Si lines in the spectrum of a solar-type star, precise Si abundances are easier to obtain, and so we favour using Si here.

7 N. C. Santos et al.: Constraining planet structure and composition from stellar chemistry: trends in diﬀerent stellar populations

Figure C.1. Upper panel: values of firon (upper panel) as a function of [Si/Fe]. Middle and lower panels: Z as a function of two different index values as defined in the text. Different galactic populations are denoted with different symbols. The lines denote linear cubic fits to the data.